Paradoxes are interesting things. The following paradox was invented by Bertrand Russell : A certain male barber shaved all and only those men in his town who didn't shave themselves. In other words, he shaved every man who didn't shave himself, but never shaved anyone who shaved himself. The question is this: Did the barber shave himself or didn't he? Well, suppose he shaved himself. Then he is one of the men who shaved himself, but he never shaved such a man, hence this is impossible! On the other hand, suppose he didn't shave himself. Then he is one of the men who didn't shave himself, but he must shave every such man! Thus we get a contradiction either way! What is the way out? Answer will be given in the next posting.

The way out is:

The bearded barber must shave himself only once, at which point he is self-shaved and can't ever shave again.
Poor guy.

The solution to the barber paradox is so obvious that it tends to get overlooked! Now look, suppose I told you that a certain person was more than six feet tall and less than six feet tall--how would you explain that? The only rational explanation is that I must obviously be either mistaken or lying! There couldn't possibly be such a person. Similarly, there couldn't possibly be a barber of the sort described. Thus the answer is that there is no such barber.

_________________"Simplicity is the highest goal, achievable when you have overcome all difficulties." ~ Frederic Chopin

The following cute paradox was invented by the literary agent Lisa Collier: The president of a certain firm offered a hundred dollars as a reward to any employee who could suggest an idea that would save the firm money. One employee wrote: "Eliminate the reward!"

Another cute one: The six year old daughter of a certain philosopher once said to him:
"Daddy, I thought of a paradox--a parent who tells his child 'Don't do what I tell you!' "

_________________"Simplicity is the highest goal, achievable when you have overcome all difficulties." ~ Frederic Chopin

Paradoxes are interesting things. The following paradox was invented by Bertrand Russell : A certain male barber shaved all and only those men in his town who didn't shave themselves. In other words, he shaved every man who didn't shave himself, but never shaved anyone who shaved himself. The question is this: Did the barber shave himself or didn't he? Well, suppose he shaved himself. Then he is one of the men who shaved himself, but he never shaved such a man, hence this is impossible! On the other hand, suppose he didn't shave himself. Then he is one of the men who didn't shave himself, but he must shave every such man! Thus we get a contradiction either way! What is the way out? Answer will be given in the next posting.

Define 'HIS' town. Does it mean the town where his barber shop is, or the town where he lives? It wouldn't be a paradox if he lives in a different town from where he works.

Last edited by Adam on Tue Jan 08, 2008 6:57 pm, edited 2 times in total.

--Is it possible for a person to have great grandchildren if none of his grandchildren have any children? Well, I know someone who has great grandchildren and yet none of his grandchildren have any children! How do you explain that? [The answer will be given in the next posting.]

_________________"Simplicity is the highest goal, achievable when you have overcome all difficulties." ~ Frederic Chopin

--Is it possible for a person to have great grandchildren if none of his grandchildren have any children? Well, I know someone who has great grandchildren and yet none of his grandchildren have any children! How do you explain that? [The answer will be given in the next posting.]

Sadly, one or more of the grandchildren have died after producing the great grandchildren.

But depending on how you define 'having children', the grandchildren could have adopted children, or married someone with children from a previous marriage. So that they would have children in the juridical sense but not in the biological sense.

How can it be possible that my friend has great grandchildren and yet none of his grandchildren have any children? The answer is that he has grandchildren and those kids are really GREAT! [Pretty sneaky, huh?]

_________________"Simplicity is the highest goal, achievable when you have overcome all difficulties." ~ Frederic Chopin

Another sneaky one: Two brothers Bob and Bill. Bob claims to have twice as many girl friends as Bill. Bill says that they have the same number of girl friends. Could they both be right? [Answer on next posting.]

_________________"Simplicity is the highest goal, achievable when you have overcome all difficulties." ~ Frederic Chopin

Another sneaky one: Two brothers Bob and Bill. Bob claims to have twice as many girl friends as Bill. Bill says that they have the same number of girl friends. Could they both be right? [Answer on next posting.]

Sneaky Bob is dating all of Bill's girlfriends without poor Bill knowing it.

Another sneaky one: Two brothers Bob and Bill. Bob claims to have twice as many girl friends as Bill. Bill says that they have the same number of girl friends. Could they both be right? [Answer on next posting.]

No, that doesn't work. There is a much more straightfotward solution! It dorsn't have to be girl friends. Look, it could just as well be the following: Bob claims to have twice as much money as Bill, and Bill says that they both have the same amount of money, yet both of them are right. How can that be?

No, that doesn't work. There is a much more straightfotward solution! It dorsn't have to be girl friends. Look, it could just as well be the following: Bob claims to have twice as much money as Bill, and Bill says that they both have the same amount of money, yet both of them are right. How can that be?

No, that doesn't work. There is a much more straightfotward solution! It dorsn't have to be girl friends. Look, it could just as well be the following: Bob claims to have twice as much money as Bill, and Bill says that they both have the same amount of money, yet both of them are right. How can that be?

I'll give you a hint: From the information given about the girl friends, one can deducr exactly how many girl frieds each one has, and in the variant I gave involving money instead of girl friends, one can deduce exactly how much money each one has!
Raymond

Last edited by rsmullyan on Thu Jan 10, 2008 8:56 pm, edited 1 time in total.

Joufa, there is no reason why in your solution, the number 4 should work better than any other number-- it could just as well be that each brother has ten, and one of the brothers folds five of them in half! I told you that from the information I gave, it is deducible exactly haw many each has, and there is only ONE possible solution!
Raymond

_________________"This is death! This is death as this emanation of the female which leads to unification ... death and love ... this is the abyss." This is not music", said [Sabaneev] to him, "this is something else..." - "This is the Mysterium," he said softly.

Juufa, No, the number 1 doesn't work. Twice 1 is not the sam as 1X1. Twice 1 is i+i, which is 2. In general, for any number n, twice n is not nXn , but n+n. For example, twice 5 is certainly not 5X5 (which is 25), but 5+5, which is 10.
Raymond

_________________"This is death! This is death as this emanation of the female which leads to unification ... death and love ... this is the abyss." This is not music", said [Sabaneev] to him, "this is something else..." - "This is the Mysterium," he said softly.

Exactly what I was thinking. He said that doesn't work, for some reason, but as far as I know, 2x0=0. Perhaps there's a more clever answer that he's looking for? But I can't get past the 0, because I don't see why it doesn't work.

Exactly what I was thinking. He said that doesn't work, for some reason, but as far as I know, 2x0=0. Perhaps there's a more clever answer that he's looking for? But I can't get past the 0, because I don't see why it doesn't work.

Yup, last time I checked, 2x0 was still zero. But you never know with today's crazy pace of science and technology... Maybe at absolute zero temperatures, things start working differently.

Raymond may have been referring to my first, contrived, 'solution'. IMO there is no more straightforward solution than the zero, but the latest hint seems to point in another direction (which I think I guessed after the hint).

I'll attach something that might keep you away from the piano for a while . Yes, you can "brute force" your way through it but it is more fun if one think first. Download and run (you need Powerpoint installed).

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